1. Field of the Invention
This invention generally relates to the field of gas detection and photonic crystal devices design, and specifically but not exclusively to gas detection and photonic crystal devices design that use numerical analysis to predict a spectral response of a photonic crystal.
2. Description of the Related Art
A photonic crystal is a periodic dielectric or metallo-dielectric (nano)structure that is designed to affect the propagation of electromagnetic waves in the same way as the periodic potential in a semiconductor crystal affects the electron motion, by defining allowed and forbidden photonic energy bands (See http://www.webster-dictionary.org/definition/Photonic%20crystalE; Yablonovitch, “Inhibited Spontaneous Emission in Solid State Physics and Electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987); S. John, “Strong Localization of Photons in Certain Disordered Dielectric Superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987); and J. D. Joannopoulos, R. D. Meade, J. N. Winn, “Photonic Crystals,” Princeton, N.J.: Princeton Univ. Press (1995)). The forbidden photonic energy band of a given photonic crystal is known as a “band gap”, and represents the frequency range at which light cannot propagate unattenuated within a photonic crystal. By altering properties of the photonic crystal, a defect may be introduced in such a way as to allow a defect mode to exist within the band gap. Since the defect is surrounded by the periodic structures possessing a band gap, light can be localized at the defect region. Resonant frequencies can then be determined by analysis within the frequency range of the band gap.
In the design of devices which use photonic crystals, it may be helpful to obtain accurate and efficient predictions of the spectral response of a photonic crystal. For example, a predicted spectral response of a photonic crystal can be compared with known spectral response data corresponding to particular photonic crystal arrangements. In addition, such analysis may be useful for predicting changes in resonant mode behavior based on physical and/or environmental changes that affect a photonic crystal device.
Several techniques have been employed to determine the frequency range of a band gap for a photonic crystal having a defect therein. Such techniques include Plane Wave Expansion (PWE), the plane wave based Transfer Matrix Method (TMM), the Finite Element Method (FEM), Finite Difference Time Domain (FDTD), and Rigorous Coupled Wave Analysis (RCWA). These techniques can produce predicted estimates of a transmission spectrum which includes the frequency range of the band gap.
Although the above-mentioned techniques (including both frequency and time domain simulations) can determine the frequency range of the band gap, they typically do not provide sufficient information for analysis of the resonant frequencies occurring within the full range of the band gap. The resonant frequencies of a photonic crystal having a defect therein are typically represented as resonant peaks within the band gap range. However, the resolution of the transmission spectrum alone is usually too low for identifying and characterizing each of these resonant peaks.
To characterize each of the resonant peaks, it is desirable to determine the position (i.e. frequency) of each resonant peak within the range of the band gap, as well as the width (e.g. FWHM), and amplitude of each peak. It should be noted that resonant peaks with a high Q factor (quality factor) are often desired, with Q being proportional to the ratio between the peak frequency and the peak width.
As noted above, the transmission spectrum (e.g., generated by numerical methods such as PWE) alone typically does not have a high enough resolution to identify and characterize the resonant peaks. Thus, performance of additional numerical simulation is often necessary to obtain a sufficiently accurate prediction of a spectral response of a photonic crystal device.
One device that can benefit from the accurate and efficient prediction of a spectral response is a gas detector device using a photonic crystal cavity. In traditional gas detectors, like the one shown in FIG. 4, a laser light is output from a laser source 401, through a gas volume 402 across a distance L. The laser output travels through a gas specimen under detection, and the laser power decays exponentially due to absorption of the gas specimen. A photo detector 403 on the other side of the gas specimen detects the remaining optical power after the absorption. By monitoring the absorption optical power, the concentration of the gas specimen between the laser source 401 and the photo detector 403 can be determined.
In addition to determining the concentration of the gas specimen, the type of gas specimen can also be estimated. This is because most gases have unique absorption wavelengths, which correspond with unique atomic and molecular compositions. FIG. 5 illustrates a graph depicting the unique absorption wavelengths of different gases. There are more extensively tabulated absorption spectra and amplitudes available in several databases (e.g. HITRAN). Therefore, by choosing a specific wavelength of laser light, certain gas compositions can be detected without interference by other gas molecules. FIG. 6 illustrates a table showing a subset of 5 gases and their unique absorption wavelengths in the near infrared (NIR) wavelength range.
Although traditional gas sensors may be capable to detect presence of a gas, the sensors tend to be large and expensive, particularly for use in applications such as automobile and consumer gas sensors. The light path of such sensors are typically long, in order to increase the absorption properties of the gas sensor and to increase sensitivity. Additionally, ongoing adjustment may be required to maintain the performance of such gas, resulting in a higher overall cost for the sensor.
If a gas sensor was to be implemented using a photonic crystal cavity structure, gas can be introduced into the cavity. Since light is localized at the cavity (or defect region), light can be absorbed by the gas in the cavity more efficiently than the single path device shown in FIG. 4.
However, in order to measure the absorption rate, an accurate prediction of the spectral response of the photonic cavity is required. This prediction is useful for determining whether gas has been absorbed, and if so, what type of gas corresponds with the absorption rate. Since the prediction could be calculated numerous times, an efficient simulation is desired.
Another device which can benefit from the accurate and efficient prediction of spectral response data is a photonic crystal device for design and analysis of photonic crystals. From a design standpoint, such a device can be used to determine whether input data representing a particular photonic crystal structure meets desired design characteristics. Alternatively, from an analysis standpoint, such a device can be used for analyzing whether a photonic crystal contains a cavity, and if so, what the cavity structure looks like.
Analysis of spectral response data in the above-described devices is made more complex when dealing with 3D photonic crystal structures. Prediction of spectral response data with sufficient detail for a 3-D photonic crystal structure can require a large amount of time (e.g., several weeks) and computational resources (e.g., supercomputers with hundreds of CPUs) using conventional analysis approaches.